I’ll check it out, but it looks like your links are all paleo propaganda. Paleo is just a repackaging of Atkins, which is discredited nonsense.
I really don't know anything about Atkins. My diet is:
1. Eat only real foods. Real foods do not have a list of ingredients
2. Eliminate all processed foods with chemicals
3. Eliminate refined sugars, esp. HFCS
4. Eliminate all grains.
So I suggest you eat lots of natural foods - meats, dairy, eggs, vegetables, legumes. I eat fruit, but never drink fruit juice (This concentrates the sugars.) I only eat hormone free, grass fed meats. Free range chicken and eggs. Natural foods. I eat everything I want, and as I mentioned, I went from 215 to 170, and dropped 4 inches of belly fat in 2 years. My bp is 110/65, and I have a resting heart rate of 53. I do work out (racquetball) 6 days a week.